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In the original statement of the problem, Monty knows what is behind each door. If he selected the door at random, the point of the problem is moot.


It's not just that he knows, but that he uses that knowledge to pick a door instead of choosing a door at random.

But yeah, that the problem is moot if it were random is exactly my point.

I was deceived by the wording and it's frustrating to hear "answers" to this problem that ignore that deception because I got the wrong answer and so I feel "dumb" for being decieved so I am trying to defend how i'm not "dumb" for not seeing the probability, just dumb for not thinking through the fact that it would be unlikely for Monty to reveal a car at that point.

I guess a lot of people go "oh, he won't reveal a car".

I'm missing that intuition.


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